Experimental Certification of a Minimal Informationally Complete Positive Operator-Valued Measure in a Device-Independent Protocol*

Minimal informationally complete positive operator-valued measures (MIC-POVMs) are a special kind of measurements in quantum theory that have the property that the statistics of their d²-outcomes are enough to reconstruct any d-dimensional quantum state. For this reason, MIC-POVMs are referred to as "standard" measurements for quantum information, and are of the utmost interest in quantum information theory and applications, where they have been shown to be the ultimate tools for quantum state tomography [1], quantum key distribution [2] and randomness certification [3], among other fields.
We report on an experiment with entangled photon pairs that certifies for the first time a MIC-POVM for qubits following a device-independent protocol. That is, modeling the state preparation and the measurement devices as black boxes and using only the statistics of the inputs and outputs.

1. J. Reháček et al., PRA 70, 052321 (2004)
2. C. A. Fuchs et al., Quantum Information and Computation 3, 377 (2003)
3. A. Acín et al., PRA 93, 040102(R) (2016)